Abstract
This work focus on the simulation of gas pipeline dynamic models in view to develop a leakage detection tool. The gas dynamics in the pipes is represented by a system of nonlinear partial differential equations. The linear partial differential equations is reduced to a transfer function model. Taking advantage of an electrical analogy, a pipeline can be represented by a two port network where gas mass flows behave like electrical currents and pressures like voltages. Thence, four transfer functions quadripole models are found to describe the gas pipeline dynamics, depending on the variable of interest at the boundaries. These models are simple enough to be used in the control and management of the network. These models have been validated using operational data and used to simulate a leakage. © Copyright 2016, PSIG, Inc.

Abstract
In this article, the problem of deriving a physical model of a mechanical structure from an arbitrary state-space realization is addressed. As an alternative to finite element formulations, the physical parameters of a model may be directly obtained from identified parametric models. However, these methods are limited by the number of available sensors and often lead to poor predictive models. Additionally, the most efficient identification algorithms retrieve models where the physical parameters are hidden. This last difficulty is known in the literature as the inverse vibration problem. In this work, an approach to the inverse vibration problem is proposed. It is based on a similarity transformation and the requirement that every degree of freedom should contain a sensor and an actuator (full instrumented system) is relaxed to a sensor or an actuator per degree of freedom, with at least one co-located pair (partially instrumented system). The physical parameters are extracted from a state-space realization of the former system. It is shown that this system has a symmetric transfer function and this symmetry is exploited to derive a state-space realization from an identified model of the partially instrumented system. A subspace continuous-time system identification algorithm previously proposed by the authors in [1] is used to estimate this model from the IO data.

Abstract
In this paper, the gas dynamics within the pipelines is modelled as a repetitive process with smoothing. Controllability and observability criteria when the system is steered through initial and boundary data, which is achieved by an adequate choice of the homogeneity, are obtained. From the point of view of the technical applications, it seems to make more sense to consider boundary data controls as for instance in the management of high pressure gas networks. Stability criteria suitable computer simulations are also included.

Abstract
This article presents four state-space models for high pressure gas pipelines, departing from a system of nonlinear partial differential equations. The models were derived taking advantage of an electrical analogy and are very accurate and simple, therefore suitable for network simulation and analysis. The models' simulation is compared with the data obtained with Simone (R), a commercial simulator of gas transport and distribution networks used by many european companies, and exhibit similar accuracy.

Abstract
In this article, an algorithm to identify LPV State Space models is proposed. The LPV State Space system is in the companion reachable canonical form. Both the state matrix and the output vector coefficients are linear combinations of a set of nonlinear basis functions dependent on the scheduling signal. This model structure, although simple, can describe accurately the behaviour of many nonlinear systems by an adequate choice of the scheduling signal. The identification algorithm minimises a quadratic criterion of the output error. Since this error is a linear function of the output vector parameters, a separable nonlinear least squares approach is used to minimise the criterion function by a gradient method. The derivatives required by the algorithm are the states of LPV systems that need to be simulated at every iteration. The effectiveness of the algorithm is assessed by two simulated examples.

Abstract
In this paper we introduce a bilinear repetitive process and present an iterative subspace algorithm for its identification. The advantage of the proposed approach is that it overcomes the "curse of dimensionality", a hurdle commonly encountered with classical bilinear subspace identification algorithms. Simulation results show that the algorithm converges quickly and provides new alternatives for modeling/identifying nonlinear repetitive processes.